SOLUTION: The expression f(x)=x^3+ax^2+bx-6 is exactly divisible by (x-1), and has a remainder of 20 when it is divided by (x-2). Calculate the value of a and b.

Algebra ->  Expressions -> SOLUTION: The expression f(x)=x^3+ax^2+bx-6 is exactly divisible by (x-1), and has a remainder of 20 when it is divided by (x-2). Calculate the value of a and b.       Log On


   

Question 695456: The expression f(x)=x^3+ax^2+bx-6 is exactly divisible by (x-1), and has a
remainder of 20 when it is divided by (x-2). Calculate the value of a and b.
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
f%281%29+=+1%5E3%2B+a%281%29%5E2+%2B+b%281%29+-6+=+a+%2B+b+-5+
f(1) = 0 therefore a + b = 5
f%282%29+=+2%5E3%2B+a%282%5E2%29+%2B+b%282%29+-6+=+4a+%2B+2b+%2B+2+
f(2) = 20 therefore 4a + 2b + 2 = 20, transpose 2 then divide by -2
The result is -2a - b = -9, add to a + b = 5
The result is -a = -4, therefore a = 4 and b = 1.
Answer: a = 4 and b = 1